PRINCIPIA · THEOREM

Pythagorean theorem

Depends on: Geometric mean / altitude-on-hypotenuse theorem.

Statement

Let right $\triangle ABC$ have $\angle C = 90^\circ$ , and denote the side lengths

a = |BC|,\qquad b = |CA|,\qquad c = |AB|

(so $a$ , $b$ are the two legs and $c$ is the hypotenuse). Then

a^{2} + b^{2} \;=\; c^{2}.

$Right \triangle ABC (\angle C=90^\circ) + the three squares a^2, b^2, c^2 on the three sides; the area relation a^2+b^2=c^2.$

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